MAT1511 Assignment 2 (Answers) Semester 1 - 2023

MAT1511 Assignment 2 (Answers) Semester 1 - 2023 Questions asked: 1. Write (2+3i) (4−3i) (3+2i) 2 (4) in the form a+bi, where a,b ∈ R. 2. Given z1 = 2∠180o , ; z2 = 3∠270o and z3 = 1∠180o . Determine the following and leave your answers in rectangular form: (i) (z1) 2 +z2 z2 +z3 (5) (ii) z1 z2z3 (5) 3. Let Z = −1− √ 3i (i) Write Z in a polar form (2) (ii) Use De Moivre’s Theorem to determine Z 4 . (3) Z and leave your answer in polar form with the angle in radians (a) Z = 1−i √ 3 2 (5)  2, 5π 4  ,  2,− 5π 4  ,  −2,− π 4  . (3) (b) Convert into rectangular coordinates:  −4,− 13π 6  . (3) 4 4. Use De Moivre’s Theorem to determine the cube root of 5. (a) Plot the following points in the same polar coordinates system MAT1511/101/0/2023 (c) Convert the following rectangular coordinates into polar coordinates (r,θ) so that r ≥ 0 and −2π ≤ θ ≤ 2π : √ 3,−1  . (3) 35.0m/s through a pipe that is at an angle of 75o with the horizontal. What are the components of its velocity? (3) F1 = −2i +2j, F2 = i −6j, F3 = 3i −5j. Determine F4 and its magnitude. (4) 15 km/h crosswind flowing in the direction S30oW. (a) Find the speed the aeroplane. (7) (b) Determine the directionof the aeroplane. (Leave your answer in terms of square root)(3) [TOTAL: 50]